Over the past thirty years, camera acquisition of a golfer's club movement and ball launch conditions have been patented and improved upon. An example of one of the earliest high speed imaging systems is U.S. Pat. No. 4,136,387, entitled “Golf Club Impact and Golf Ball Monitoring System,” issued in 1979. This automatic imaging system employed six cameras to capture pre-impact conditions of the club and post impact launch conditions of a golf ball using retroreflective markers. In an attempt to make such a system portable for outside testing, patents such as U.S. Pat. Nos. 5,471,383 and 5,501,463 to Gobush disclosed a system of two cameras that could triangulate the location of retroreflective markers appended to a club or golf ball in motion.
These systems allowed the kinematics of the club and ball to be measured. Additionally, these systems allowed a user to compare their performance using a plurality of golf clubs and balls. Typically, these systems include one or more cameras that monitor the club, the ball, or both. By monitoring the kinematics of both the club and the ball, an accurate determination of the ball trajectory and kinematics can be determined.
A recent patent, U.S. Pat. No. 6,758,759, entitled “Launch Monitor System and a Method for Use Thereof,” issued in 2004, describes a method of monitoring both golf clubs and balls in a single system. This resulted in an improved portable system that combined the features of the separate systems. The use of fluorescent markers in the measurement of golf equipment was added in U.S. published patent application. No. 2002/0173367 A1.
Monitoring both the club and the ball requires complicated imaging techniques. Additionally, complicated algorithms executed by powerful processors are required to accurately and precisely determine club and ball kinematics. Furthermore, these systems are typically unable to quickly determine which combination of club and balls produces the best outcome for a particular player. Presently, the only way to accomplish this was to test a golfer with a variety of different clubs and/or balls, and then monitor which combination resulted in the most desirable ball trajectory.
The need for a mathematical tool for evaluating golf club performance is dictated by the large number of club design parameters and initial conditions of the impact between club head and ball. Without such a tool, it is not feasible to make quantitative predictions of the effects of a design change on the ball motions and shaft stresses.
For example, in stereo mechanical impact, as described in U.S. Pat. No. 6,821,209 to Manwaring et al., the final velocities and spin rates can be related to the initial values of these quantities without considering the changes that occurred during impact between the club head and the ball, e.g., about 500 microseconds. However, by eliminating the details from the impact between the club and the ball, the stereo mechanical impact approach assumes that: (1) the three components of the relative velocity of recession of the ball from the club head can be related to those of the approach of the club to the ball, as measured at the impact point, by “coefficient of restitution” and; (2) the shaft can be considered completely flexible, like a stretched rubber band, as far as the dynamics of impact are concerned, so that no dynamic changes occur in the force or torque that it exerts on the club head during the impact.
The stereo mechanical approximation problem involves a set of 12 simultaneous linear algebraic equations in the 12 unknown components of motion of the ball and club after impact. The known quantities in these equations are the initial conditions, i.e., club head motions and impact point coordinates, and the many mechanical parameters of the club head and golf ball, e.g., masses, mass moments of inertia, centers of mass, face loft angle, and face radii of curvature. The explicit algebraic expressions are described in the '209 patent to Manwaring et al.
The stereo mechanical approximation has drawbacks, such as (1) the effects of the shaft on the impact, although small, are not negligible, and it is desirable to obtain quantitative measures of these effects for shaft design purposes; (2) shaft stresses cannot be computed in any realistic manner; (3) the explicit algebraic expressions obtained are still too complex to permit assessments to be made of the effects of design parameter changes except by working out many specific cases with the aid of a computer; and (4) the coefficient of restitution approximation may not be accurate because the sliding and sticking time of the ball at the impact point is not taken into account. In addition, the coefficient of restitution approximation is poor because different amounts of stress wave energy may be “trapped” in the shaft under different impact conditions.
Impact forces can also be measured. Measurements and instrumentation to measure normal and transverse forces on golf balls was described in Gobush, W. “Impact Force Measurements on Golf Balls,” pp. 219-224 in Science and Golf, published by E. F. Spoon, London, 1990. Although the piezoelectric sensor instrument measured these forces and result in explanation of the nature of the normal and transverse force, the transducer noise was found to cause spurious signals that resulted in low accuracy estimates of spin rate and contact time. With newer methods to measure contact time and coefficient of restitution as described in U.S. Pat. No. 6,571,600 to Bissonnette et al. a renewed effort was implemented in estimating these forces from impacting golf balls with a steel block.
In an effort to improve the accurate modeling of the contact between the club and the ball, a model published by Dr. Ralph Simon, titled “The Development of a Mathematical Tool for Evaluating Golf Club Performance,” ASME Design Engineering Conference, New York, May 1967 (pages 17-35) was improved and updated mathematically. In addition, the modeling may also be implemented by a golf ball model described in the paper titled “Spin and the Inner Workings of a Golf Ball,” by W. Gobush, 1995, in a book titled Golf the Scientific Way, edited by Cochran, A., Aston Publishing Group, Hertfordshire. Both models were shown to give roughly equivalent results on studies of a golf ball hitting a steel block. These two references are incorporated herein by reference in their entireties.
Further modeling of transverse impact is described by Johnson, S. H. and Lieberman, B. B. titled “An Analytical Model for Ball-barrier impact”, pp. 315-320, Science and Golf II, published by E. F. Spoon, London, 1994. A further experimental assessment of this model was presented in “Experimental Study of Golf Ball Oblique Impact” by S. H. Johnson and E. A. Ekstrom in Science and Golf III, pp. 519-525.
A method for measuring the coefficient of friction between golf ball and plate is described in Patent Application US2006/0272389 A1. This quantity is useful in modeling the collision process when sliding becomes predominant in the collision process. Experimental methods for measuring the coefficient of sliding friction are described in “Experimental Determination of Golf Ball Coefficients of Sliding Friction” by Johnson, S. H. and Ekstrom, E. A., pp. 510-518, Science and Golf, edited by Farally, M. R. and Cochran, A. J., published by Human Kinetics, 1999. Also, coefficient of friction measurements are discussed in a paper by Gobush, W. titled “Friction Coefficient of Golf Balls,” the Engineering of Sport, edited by Haake, Blackwell Science, Oxford (1996).
Therefore, a continuing need exists for a system that is capable of determining or modeling the trajectory and launch conditions of a golf ball. Moreover, a continuing need exists for a system that includes software that reduces the complexity associated with fitting a golfer with golf equipment, and for a system that more accurately predicts a golfer's ball striking performance.